Question

20. A spherical shell of lead whose external and internal diameters are 24 cm and 18 cm, is melted and recast into a right circular cylinder 37 cm high. Find the diameter of the base of
the cylinder.​

Answer 1

Answer:

Diameter of the base is 12 cm

Step-by-step explanation:

External diameter of the shell = 24 cm

External radius of the shell $r_1=12$ cm

Internal diameter of the shell = 18 cm

Internal radius of the shell $r_2=9$ cm

Volume of the lead in the shell

=Volume of the external shell - Volume of the internal shell

$=\frac{4}{3}\pi r_1^3-\frac{4}{3}\pi r_2^3$

$=\frac{4}{3}\pi (r_1^3-r_2^3)$

$=\frac{4}{3}\pi (12^3-9^3)$

$=1332\pi$ cm^3

Height of the right circular cylinder $h=37$ cm

If the radius of the cylinder is r then

The volume of the cylinder = Volume of the lead

$\pi r^2h=1332\pi$

$\implies r^2\times 37=1332$

$\implies r^2=36$

$\implies r=\sqrt{36}$

$\implies r=6$ cm

Thus, the diameter of the base

$=2r$

$=2\times 6$

$=12$ cm

Hope this helps.

Answer 2

Diameter of the base of cylinder is 12 cm.